
where the \(W_p\)  and \(b_p\)  are the learnable parameters.
It is worth noticing that some works [1]}, [2]}, [3]}, [4]} also attempt to append one more LSTM layer to predict the word, please refer [1]} for details.
Finally, given a target ground truth sequence \(y_{1: T}^{*}\)  and a captioning model with parameters \(\theta \) , the objective is to minimize the following cross entropy loss:
\(\footnotesize \mathcal {L}_{\textrm {CE}}(\theta )=-\sum _{t=1}^{T} \log \left(p_{\theta }\left(y_{t}^{*} | y_{1: t-1}^{*}\right)\right) .\) 
